This set of Aptitude Questions and Answers (MCQs) focuses on “Spheres and Hemispheres”.

1. Which of the following is the correct formula for the volume of a sphere?

a) (4 / 9) * π * r^{3}

b) (2 / 9) * π * r^{3}

c) (4 / 3) * π * r^{3}

d) (2 / 3) * π * r^{3}

View Answer

Explanation:

Let the radius of the sphere be r.

The correct formula for the volume of a sphere of radius r = (4 / 3) * π * r

^{3}.

2. What will be the radius of a spherical vessel having a volume of 5600 cm^{3}?

a) 11 cm

b) 12 cm

c) 9 cm

d) 13 cm

View Answer

Explanation: Given,

Volume of spherical vessel = (4 / 3) * π * r

^{3}

➩ 5600 cm

^{3}= (4 / 3) * π * r

^{3}

➩ 5600 = (4 / 3) * (22 / 7) * r

^{3}

➩ 5600 * 3 * 7 / (4 * 22) = r

^{3}

➩ 117600 / 88 = r

^{3}

➩ 1336.36 = r

^{3}

➩ r = 11 cm

3. Which of the following is the correct option expressing the volume of a hemisphere?

a) (2 / 9) * π * r^{3}

b) (2 / 3) * π * r^{3}

c) (4 / 3) * π * r^{3}

d) (4 / 9) * π * r^{3}

View Answer

Explanation: Let the radius of the hemisphere be r.

Correct formula for the volume of a hemisphere = (2 / 3) * π * r

^{3}.

4. If two solid hemispheres of same base radii as (3 / 2) r, are joined together along their bases, then what would be the curved surface area of this new solid?

a) 9πr^{2}

b) 12πr^{2}

c) 16πr^{2}

d) 6πr^{2}

View Answer

Explanation:

Curved surface area of a solid hemisphere = 2 * π * ((3 / 2) r)

^{2}

Thus, curved surface area of new solid = 2 * (2 * π * (9 / 4) r

^{2})

= 9πr

^{2}

5. What is the volume (in cubic cm) of a hemispherical bowl of radius 12 cm?

a) 1331π

b) 1420π

c) 1152π

d) 1519π

View Answer

Explanation: Given,

r = 12 cm

Volume of hemisphere = (2 / 3) * πr

^{3}

= (2 / 3) * π * (12)

^{3}

= 1152π

6. If the radius of a sphere is made five times, what will be the ratio of the volume of new sphere to the ratio of volume of original sphere?

a) 5:1

b) 25:1

c) 1:625

d) 125:1

View Answer

Explanation: Let the radius of original sphere = r

Volume of original sphere = (4 / 3) * πr

^{3}

Radius of new sphere = 5r

Volume of new sphere = (4 / 3) * π * (5r)

^{3}

= (4 / 3) * 125πr

^{3}

Ratio = Volume of new sphere / Volume of original sphere

= ((4 / 3) * 125πr

^{3}) / ((4 / 3) * πr

^{3})

= 125:1

7. If the radius of a hemisphere is reduced to half, then, how many times is the volume of the new hemisphere to original hemisphere?

a) 1 / 8 times

b) 1 / 2 times

c) 1 / 4 times

d) 1 / 16 times

View Answer

Explanation: Let the side of the original hemisphere = r

Volume of original hemisphere = (2 / 3) * πr

^{3}

The side of new hemisphere = (1 / 2) r

Volume of new hemisphere = (2 / 3) * π * ((1 / 2) r)

^{3}

Thus, on comparing,

The volume of new hemisphere is (1 / 8) times the original hemisphere.

8. A hemispherical bowl has a radius of 7 cm. How much cubic cm of water will this bowl contain if its half-filled?

a) 765.46

b) 723.22

c) 718.66

d) 732.99

View Answer

Explanation: Given,

r = 7 cm

Volume of hemisphere = (2 / 3) * πr

^{3}

= (2 / 3) * (22 / 7) * (7)

^{3}

= 718.66 cm

^{3}

9. Two sphere of radius 2 cm each are melted and casted into a single sphere. What would be the radius of this new sphere?

a) 4 cm

b) 16^{1/3} cm

c) 12^{1/3} cm

d) 2 cm

View Answer

Explanation: Given,

r = 2 cm, let the radius of new sphere = R

According to the question

2 * ((4 / 3) * πr

^{3}) = (4 / 3) * πR

^{3}

2 * ((4 / 3) * π (2)

^{3}) = (4 / 3) * πR

^{3}

2 * 8 = R

^{3}

R = 16

^{1/3}cm

10. What will be the volume of a sphere having radius as 21 cm?

a) 38,808 cm^{3}

b) 14,400 cm^{3}

c) 28,562 cm^{3}

d) 49,263 cm^{3}

View Answer

Explanation: Given,

r = 21 cm

Volume of sphere = (4 / 3) * πr

^{3}

= (4 / 3) * (22 / 7) * (21)

^{3}

= 38,808 cm

^{3}

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